How can I determine which version of Excel was used to create a .xls file?

Microsoft KB 178605: How To Determine the Version of a Microsoft Excel Workbook (snapshot)

Microsoft Excel saves data using structured storage. In particular, it creates a data stream called "Workbook" (previously just "Book") where it saves the contents starting with a BOF (beginning of file) record. This record contains useful attributes of the workbook, as well as the version.

That article goes on to give sample C++ code to dump this information.

Also see, Stackoverflow,
How to identify whether an Excel file conforms to Excel 95 or Excel 97 specifications?

You could also save the excel file with the .zip extension. Then open that archive and look in the docProps folder. Open the app.xml and check the AppVersion node:

16.0300